{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AGENOU7EXGCVJQ4BUSRKVI52LO","short_pith_number":"pith:AGENOU7E","schema_version":"1.0","canonical_sha256":"0188d753e4b98554c381a4a2aaa3ba5ba10faf24ab3c9d4a8558f5a2fdb93dae","source":{"kind":"arxiv","id":"1507.00969","version":2},"attestation_state":"computed","paper":{"title":"An FPTAS for Minimizing Indefinite Quadratic Forms over Integers in Polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kevin Zemmer, Robert Hildebrand, Robert Weismantel","submitted_at":"2015-07-03T17:00:36Z","abstract_excerpt":"We present a generic approach that allows us to develop a fully polynomial-time approximation scheme (FTPAS) for minimizing nonlinear functions over the integer points in a rational polyhedron in fixed dimension. The approach combines the subdivision strategy of Papadimitriou and Yannakakis (2000) with ideas similar to those commonly used to derive real algebraic certificates of positivity for polynomials. Our general approach is widely applicable. We apply it, for instance, to the Motzkin polynomial and to indefinite quadratic forms $x^T Q x$ in a fixed number of variables, where $Q$ has at m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.00969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-03T17:00:36Z","cross_cats_sorted":[],"title_canon_sha256":"d19b612f134d4cc6e9f26b3da0ef72f4735b6474fe4f483f7f034be141a3b656","abstract_canon_sha256":"be7bdfadf8e30ff5a990bd01b24affbfc36e6f5cbef44992a3f2c69a87bcd8c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.056395Z","signature_b64":"OMJF+IA0UrKmyKqwQC+wl3YDprb498LNkOOwNLwzmu8r0rrUZzwy7NiafXqu+f5gH7+AMn9IWQYgvnXsa/GjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0188d753e4b98554c381a4a2aaa3ba5ba10faf24ab3c9d4a8558f5a2fdb93dae","last_reissued_at":"2026-05-18T01:30:15.055699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.055699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An FPTAS for Minimizing Indefinite Quadratic Forms over Integers in Polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kevin Zemmer, Robert Hildebrand, Robert Weismantel","submitted_at":"2015-07-03T17:00:36Z","abstract_excerpt":"We present a generic approach that allows us to develop a fully polynomial-time approximation scheme (FTPAS) for minimizing nonlinear functions over the integer points in a rational polyhedron in fixed dimension. The approach combines the subdivision strategy of Papadimitriou and Yannakakis (2000) with ideas similar to those commonly used to derive real algebraic certificates of positivity for polynomials. Our general approach is widely applicable. We apply it, for instance, to the Motzkin polynomial and to indefinite quadratic forms $x^T Q x$ in a fixed number of variables, where $Q$ has at m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00969","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.00969","created_at":"2026-05-18T01:30:15.055792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00969v2","created_at":"2026-05-18T01:30:15.055792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00969","created_at":"2026-05-18T01:30:15.055792+00:00"},{"alias_kind":"pith_short_12","alias_value":"AGENOU7EXGCV","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AGENOU7EXGCVJQ4B","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AGENOU7E","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO","json":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO.json","graph_json":"https://pith.science/api/pith-number/AGENOU7EXGCVJQ4BUSRKVI52LO/graph.json","events_json":"https://pith.science/api/pith-number/AGENOU7EXGCVJQ4BUSRKVI52LO/events.json","paper":"https://pith.science/paper/AGENOU7E"},"agent_actions":{"view_html":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO","download_json":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO.json","view_paper":"https://pith.science/paper/AGENOU7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00969&json=true","fetch_graph":"https://pith.science/api/pith-number/AGENOU7EXGCVJQ4BUSRKVI52LO/graph.json","fetch_events":"https://pith.science/api/pith-number/AGENOU7EXGCVJQ4BUSRKVI52LO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO/action/storage_attestation","attest_author":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO/action/author_attestation","sign_citation":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO/action/citation_signature","submit_replication":"https://pith.science/pith/AGENOU7EXGCVJQ4BUSRKVI52LO/action/replication_record"}},"created_at":"2026-05-18T01:30:15.055792+00:00","updated_at":"2026-05-18T01:30:15.055792+00:00"}